Heavy-Tailed Distributions: Properties and Tests

Bryson, Maurice C.

doi:10.2307/1267493

Cited by 68 publications

(67 citation statements)

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“…A graphical test attributable to Bryson (1974) solidly rejected the hypothesis that the distribution for patents valued at DM 5 million or more was negative exponential, Weibull, or any less skew variant. See also D'Agostino and Stephens (1986, Chapter 2).…”

Section: Resultsmentioning

confidence: 99%

Exploring the Tail of Patented Invention Value Distributions

Harhoff¹,

Scherer

Vopel

2003

Economics, Law and Intellectual Property

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*Patent renewal studies reveal a highly rightward-skewed distribution of patent values. Our approach elicits valuations approximating those of the patented invention. This paper focuses on the full-term patents of the application year 1977 held by West German and U.S. residents. The tail of skewed distributions values account for a large fraction of the cumulative value over all observations. Several tests were conducted to pin down more precisely the nature of the high-value tail distribution. Three highly skew alternatives were evaluated by graphical and maximum likelihood techniques: the two-parameter log normal, the one-parameter Pareto-Levy, and the three-parameter Singh-Maddala distribution. A two-parameter log normal distribution appears to provide the best fit to our patented invention value data. ZUSAMMENFASSUNG Non-technical SummaryAssessing value of patent protection has long been a central issue in the economic literature studying the incentives for innovation in market economies. A number of authors have exploited a particular feature of many (though not all) national patent systems: the renewal fee structure. In many countries, patent holders need to pay annual renewal fees in order to keep patent protection in force. The fees are usually increasing over time in order to weed out less important patents. Using information on the timing of non-renewal, some studies have been able to infer the value of patent protection.However, these studies cannot use observable information on value differences among those patents that were renewed for the maximum duration of patent protection. But these are presumably the most important patented inventions. Since the valuation distributions are extremely skew, actually observed information in most renewal studies is only available on a small share of the total value of the overall national patent portfolio.We circumvent this problem by using a novel and more direct approach to the measurement of patent valuation. The paper focuses on the full-term patents of the application year 1977 held by West German and U.S. residents. For the German patents, a two-stage methodology was pursued. A preliminary telephone and telefax screening elicited patent value estimates and identified the most valuable patents, about which on-site interviews were then sought to develop more detailed historical information. For the U.S. patents, only an extended first stage was executed.Previous studies have found the distribution of patented invention values to be highly skew. We confirm this result, using actual information on the most valuable patents in the 1977 cohort. Several tests were conducted to pin down more precisely the nature of the high-value tail distribution. Three highly skew alternatives were evaluated by graphical and maximum likelihood techniques: the two-parameter log normal, the one-parameter ParetoLevy, and the three-parameter Singh-Maddala distribution. A two-parameter log normal distribution appears to provide the best fit to our patented invention value data.

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Section: Resultsmentioning

confidence: 99%

Exploring the Tail of Patented Invention Value Distributions

Harhoff¹,

Scherer

Vopel

2003

Economics, Law and Intellectual Property

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“…The data are provided by Hogg and Klugman (1983, p.92), and we have subtracted 5million from each of their sample values, so allowing for the scale of the data reported by those authors, our first datum is 1766.0, etc. The second set of data consists of observations for precipitation in a Florida meteorological study by Simpson (1972), and further analyzed by Bryson (1974 Table 2 reports the MLEs and the bias-adjusted MLEs when the Lomax distribution is fitted to each of these three data-sets. Each of the estimates based on are less than the values of *  for the respective sample sizes, so our rule of thumb from section 5 suggests that the bias-adjusted estimates based on  and  should be used.…”

Section: Illustrative Applicationsmentioning

confidence: 99%

“…It has also found application in the biological sciences and even for modelling the distribution of the sizes of computer files on servers (Holland et al, 2006). Some authors, such as Bryson (1974), have suggested the use of this distribution as an alternative to the exponential distribution when the data are heavy-tailed. useful to incorporate a location parameter, but we do not pursue that here.…”

Section: Introductionmentioning

confidence: 99%

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

Giles

Feng

Godwin

2013

Communications in Statistics - Theory and Methods

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The Lomax (Pareto II) distribution has found wide application in a variety of fields. We analyze the second-order bias of the maximum likelihood estimators of its parameters for finite sample sizes, and show that this bias is positive. We derive an analytic bias correction which reduces the percentage bias of these estimators by one or two orders of magnitude, while simultaneously reducing relative mean squared error. Our simulations show that this analytic bias correction outperforms a correction based on the parametric bootstrap. Three examples with actual data illustrate the application of our methods.

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“…In the lifetime, the Lomax model belongs to the family of decreasing failure rate by Chahkandi et al [11] and arises as a limiting distribution of residual lifetimes at great age by Balkema et al [7]. This distribution has been proposed as heavy tailed alternative to the exponential, Weibull and gamma distributions by Bryson [8]. Moreover, it is related to the Burr family of distributions as in Tadikamalla [27].…”

Section: Introductionmentioning

confidence: 99%

Exponential Lomax Distribution

El-Bassiouny¹,

Abdo²,

Shahen³

2015

IJCA

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In this paper, A new distribution called Exponential Lomax distribution is introduced. It is seemed that the parameter values of our new distribution are depending on decreasing and upside-down bathtub failure rate function. Also, the statistical properties of this model are studied, such as, quantiles, moments, mean deviation. Moreover, maximum likelihood estimators of it ' s parameters are discussed. Finally, the procedure is illustrated by real data set. It is shown that the introduced model is more competitive than other models.

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Heavy-Tailed Distributions: Properties and Tests

Cited by 68 publications

References 0 publications

Exploring the Tail of Patented Invention Value Distributions

Exploring the Tail of Patented Invention Value Distributions

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

Exponential Lomax Distribution

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